10/15/2013, 07:14 PM
(This post was last modified: 10/15/2013, 09:32 PM by sheldonison.)

Gottfried, I think your solution is interesting. I see from your paper, that the solution you get is real valued. Presumably, there is some sort of Taylor series representation for your solution. I would be interested in seeing a Taylor series at sexp(0) where sexp(0)=1.

The Kneser solution is defined by two basic things; which your solution would need to match to converge.

1) it is real valued (it sounds like your function is also real valued).

2) the sexp limiting behavior in the complex plane, as imag(z) increases, is the same as the Schroeder function solution. At imag(z)=0.75i, it is visually the same, and convergence gets better as imag(z) increases, as defined by a 1-cyclic scaling function that goes to a constant as imag(z) increases.

- Sheldon

The Kneser solution is defined by two basic things; which your solution would need to match to converge.

1) it is real valued (it sounds like your function is also real valued).

2) the sexp limiting behavior in the complex plane, as imag(z) increases, is the same as the Schroeder function solution. At imag(z)=0.75i, it is visually the same, and convergence gets better as imag(z) increases, as defined by a 1-cyclic scaling function that goes to a constant as imag(z) increases.

- Sheldon